User subroutine for modeling transient swelling of hydrogels with Abaqus

Subjected to compressive stresses, soft polymers with stiffness gradients can display various buckling patterns. These compressive stresses can have different origins, like mechanical forces, temperature changes, or, for hydrogel materials, osmotic swelling. Here, we focus on the influence of the transient nature of osmotic swelling on the initiation of buckling in confined layered hydrogel structures. A constitutive model for transient hydrogel swelling is outlined and implemented as a user-subroutine for the commercial finite element software Abaqus. The finite element procedure is benchmarked against linear perturbation analysis results for equilibrium swelling showing excellent correspondence. Based on the finite element results we conclude that the initiation of buckling in a two-layered hydrogel structure is highly affected by transient swelling effects, with instability emerging at lower swelling ratios and later in time with a lower diffusion coefficient. In addition, for hard-on-soft systems the wavelength of the buckling pattern is found to decrease as the diffusivity of the material is reduced for gels with a relatively low stiffness gradient between the substrate and the upper film. This study highlights the difference between equilibrium and transient swelling when it comes to the onset of instability in hydrogels, which is believed to be of importance as a fundamental aspect of swelling as well as providing input to guiding principles in the design of specific hydrogel systems.while the flux of the solvent molecules in a gel was given in Equation (6). By comparing Equation (A.1) to Equation (A.3) and Equation (A.2) to Equation (6), we find that the equivalents of temperature, specific heat capacity, mass density, and conductivity can be identified asμ, ∂C ∂μ , 1 J , and CD J = J−1 vJ D respectively. These values are calculated as internal variables in the Fortran code using the USDFLD subroutine in Abaqus. The internal heat source in Abaqus, r, is set to zero.

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“…The implemented Fortran code and an example input file for Abaqus is made available as a Mendeley dataset linked to this work [58].…”

Section: Implementation and Validation Of The Constitutive Model 511 ...mentioning

confidence: 99%